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. 2017 Nov 22;7:16053. doi: 10.1038/s41598-017-14734-w

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© The Author(s) 2017

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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The influence of tip radius to the hardness. (a) Hardness curves from simulation and comparison with the theoretical hardness of conical indenter indents into elastic material. This value from continuum model stands for the upper limit of the hardness peak, equivalent to the result of R = 0 nm. (b) Hardness peak value over the tip radius. The results from experiment (black square dots), simulation (black round circles) and analytical (red round dot) seem follow the same trend, a power-law fitting curve (red dotted-line) to the data is plotted in the figure. The simulation and experiment results overlap at R = 100 nm. (c) The hardness curves from simulation (at 0 K) in terms of relatively depth (h/R). When h/R is small, the curves coincide with each other. The hardness transition occurs in spherical part of the indenter, as the hardness peaks are on the left side of the green line which indicates the boundary of spherical and conical part of the indenter. (d) The hardness curves from experiment in terms of relatively depth (h/R). Same observations can be found as these from the simulation, although the hardness and depth for the transition are higher.